Examples 4-1 PDF

Mr. Ciosici Examples 4-1 Graph the following equations by making a function table: 𝑦 = −3𝑥 + 9 2𝑦 + 5𝑥 = 20 𝑦 − 1 = 3(𝑥 + 4) 2𝑥 = 7 3𝑦 = −18 Determine (without graphing) whether the given point belongs on the graph of the indicated linear equation or not:...

Mr. Ciosici Examples 4-1 Graph the following equations by making a function table: 𝑦 = −3𝑥 + 9 2𝑦 + 5𝑥 = 20 𝑦 − 1 = 3(𝑥 + 4) 2𝑥 = 7 3𝑦 = −18 Determine (without graphing) whether the given point belongs on the graph of the indicated linear equation or not: ! (3, −4) 𝑦 = "𝑥 −5 !# % 3 $ , &4 2𝑥 − 4𝑦 = 3.9 (8,13) 5𝑥 − 12𝑦 = −116 Graph the following equations by using the x- and y-intercepts: 2𝑥 + 3𝑦 = 12 5𝑥 − 2𝑦 = 40 −3𝑥 − 4𝑦 = 17 𝑦 = 5𝑥 − 10 𝑦 = −𝑥 − 7 Graph each equation by using the x- and y-intercept, then establish what those intercepts mean: Kip goes to the movies with his buddy, Kenny. At the concession stand, a box of chocolate snacks costs $2.00, while a soda costs $3.00. Between the two of them, Kip and Kenny have $18 to spend.  Mr. Ciosici The equation for their budget is: 2𝑥 + 3𝑦 = 18 A group of students and teachers goes on a field trip to a national park. The price of a student ticket is $4.00, while the price of a teacher ticket is $6.00. The total amount of money budgeted for the field trip is $60.00. The equation for their budget is: 4𝑥 + 6𝑦 = 60  Mr. Ciosici Examples 4-1 Answers Graph the following equations by making a function table: 𝑦 = −3𝑥 + 9  Mr. Ciosici 2𝑦 + 5𝑥 = 20  Mr. Ciosici 𝑦 − 1 = 3(𝑥 + 4)  Mr. Ciosici 2𝑥 = 7  Mr. Ciosici 3𝑦 = −18  Mr. Ciosici Determine (without graphing) whether the given point belongs on the graph of the indicated linear equation or not: ! (3, −4) 𝑦 = "𝑥 −5 When we substitute 3 instead of 𝑥 and −4 instead of 𝑦 we obtain a true statement: −4 = −4. Yes, the point with the coordinates (3, −4) belongs on ! the graph of 𝑦 = " 𝑥 − 5. !# % 3 $ , &4 2𝑥 − 4𝑦 = 3.9 !# % When we substitute $ instead of 𝑥 and & instead of 𝑦 we obtain a false !# % statement: 6 ≠ 3.9. No, the point with the coordinates 3 $ , &4 does not belong on the graph of 2𝑥 − 4𝑦 = 3.9. (8,13) 5𝑥 − 12𝑦 = −116 When we substitute 8 instead of 𝑥 and 13 instead of 𝑦 we obtain a true statement: −116 = −116. Yes, the point with the coordinates (8,13) belongs on the graph of 5𝑥 − 12𝑦 = −116.  Mr. Ciosici Graph the following equations by using the x- and y-intercepts: 2𝑥 + 3𝑦 = 12  Mr. Ciosici 5𝑥 − 2𝑦 = 40  Mr. Ciosici −3𝑥 − 4𝑦 = 17  Mr. Ciosici 𝑦 = 5𝑥 − 10  Mr. Ciosici 𝑦 = −𝑥 − 7  Mr. Ciosici Graph each equation by using the x- and y-intercept, then establish what those intercepts mean: Kip goes to the movies with his buddy, Kenny. At the concession stand, a box of chocolate snacks costs $2.00, while a soda costs $3.00. Between the two of them, Kip and Kenny have $18 to spend. The equation for their budget is: 2𝑥 + 3𝑦 = 18 The x-coordinate will show the number of chocolate snacks. The y-coordinate will show the number of sodas. The x-intercept shows how many chocolate snacks they can buy if they buy no sodas. When 𝑦 = 0, 𝑥 = 9. They can buy 9 chocolate snacks. (9,0) The y-intercept shows how many sodas they can buy if they buy no chocolate snacks. When 𝑥 = 0, 𝑦 = 6. They can buy 6 sodas. (0,6)  Mr. Ciosici A group of students and teachers goes on a field trip to a national park. The price of a student ticket is $4.00, while the price of a teacher ticket is $6.00. The total amount of money budgeted for the field trip is $60.00. The equation for their budget is: 4𝑥 + 6𝑦 = 60 The x-coordinate will show the number of student tickets. The y-coordinate will show the number of teacher tickets. The x-intercept shows how many student tickets they can buy if they buy no teacher tickets (meaning no teacher goes on the field trip). When 𝑦 = 0, 𝑥 = 15. They can buy 15 student tickets. (15,0) The y-intercept shows how many teacher tickets they can buy if they buy no student tickets (meaning no student goes on the field trip). When 𝑥 = 0, 𝑦 = 10. They can buy 10 teacher tickets. (0,10)